# How do you graph #y=-3/2sinx# over #0<=x<=360#?

##### 1 Answer

May 20, 2018

See below.

#### Explanation:

Let's see how the function we want to study is obtain from the standard sine function, and how these transformation reflect on the graph:

- First of all, I assume you are familiar with the graph of the standard sine function:

graph{sin(x) [-0, 6.28, -1.5, 1.5]} - Then we must switch sign. The transformation
#f(x) -> -f(x)# affects the graph by vertical symmetry (we reflect with respect to the#x# axis:

graph{-sin(x) [-0, 6.28, -1.5, 1.5]} - Finally, we multiply the function by a constant: the transformation
#f(x) \to kf(x)# results in a vertical stretch if#k>1# , or a vertical compression otherwise. In our case, we're stretching the graph by a factor#1.5# . Note how the new maximum and minimum is not#1# anymore but#1.5#

standard sine function:

graph{-1.5*sin(x) [-0, 6.28, -2, 2]}